Non-collapsing Space-filling Designs for Bounded Non-rectangular Regions

Many researchers use computer simulators as experimental tools when physical experiments are infeasible. When computer codes are computationally intensive, nonparametric predictors can be fitted to training data for detailed exploration of the input-output relationship. The accuracy of such flexible predictors is enhanced by taking training inputs to be “space-filling”. If there are inputs that have little or no effect on the response, it is essential that the design be “non-collapsing” in the sense of having space-filling lower dimensional projections. This paper describes an algorithm for constructing space-filling designs for input regions that are bounded convex sets of possibly high dimension. On-line supplementary materials showing the performance of the algorithm accompany the paper.

[1]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[2]  C. Subramanian,et al.  Review of multicomponent and multilayer coatings for tribological applications , 1993 .

[3]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[4]  Peter Z. G. Qian.  Nested Latin hypercube designs , 2009 .

[5]  Y. C. Hung,et al.  Uniform design over general input domains with applications to target region estimation in computer experiments , 2010, Comput. Stat. Data Anal..

[6]  Yong Zhang,et al.  Uniform Design: Theory and Application , 2000, Technometrics.

[7]  Timothy W. Simpson,et al.  Sampling Strategies for Computer Experiments: Design and Analysis , 2001 .

[8]  Srikant Nekkanty,et al.  Characterization of damage and optimization of thin film coatings on ductile substrates , 2009 .

[9]  T. J. Mitchell,et al.  Exploratory designs for computational experiments , 1995 .

[10]  Elvira N. Loredo,et al.  Experimental Designs for Constrained Regions , 2002 .

[11]  M. Liefvendahl,et al.  A study on algorithms for optimization of Latin hypercubes , 2006 .

[12]  Dick den Hertog,et al.  Constrained Maximin Designs for Computer Experiments , 2003, Technometrics.

[13]  W. Welch.  ACED: Algorithms for the Construction of Experimental Designs , 1985 .

[14]  Boxin Tang.  Orthogonal Array-Based Latin Hypercubes , 1993 .

[15]  David M. Steinberg,et al.  Comparison of designs for computer experiments , 2006 .

[16]  Gregory F. Piepel,et al.  Computer-Generated Experimental Designs for Irregular-Shaped Regions , 2005 .

[17]  M. E. Johnson,et al.  Minimax and maximin distance designs , 1990 .

[18]  M. Sasena,et al.  Global optimization of problems with disconnected feasible regions via surrogate modeling , 2002 .

[19]  Garry Hayeck,et al.  THE KINEMATICS OF THE UPPER EXTREMITY AND SUBSEQUENT EFFECTS ON JOINT LOADING AND SURGICAL TREATMENT , 2009 .